On Lagrange multipliers in flexible multibody dynamics

The Lagrange multiplier technique plays a key role for the treatment of constraints in multibody systems. In contrast to the well-understood rigid body case, the formulation of constraints for elastic bodies requires special care. This paper provides an introduction to the underlying mathematical theory and shows which models are well-defined and which are questionable. Additionally, estimates on the influence of perturbations are given. A simulation example illustrates the results.

[1]  J. Lions,et al.  Inequalities in mechanics and physics , 1976 .

[2]  D. Braess.  Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics , 1995 .

[3]  Ch . Engstler,et al.  MEXX - Numerical Software for the Integration of Constrained Mechanical Multibody Systems , 1992 .

[4]  M. Arnold.  A perturbation analysis for the dynamical simulation of mechanical multibody systems , 1995 .

[5]  Gene H. Golub,et al.  Matrix computations , 1983 .

[6]  W. Han,et al.  Contact problems in elasticity , 2002 .

[7]  I. Higueras.  Numerical Methods for Stiff Index-3 DAEs , 2001 .

[8]  Peter Wriggers,et al.  Computational Contact Mechanics , 2002 .

[9]  T. R. Hughes,et al.  Mathematical foundations of elasticity , 1982 .

[10]  Olivier A. Bauchau,et al.  Robust integration schemes for flexible multibody systems , 2003 .

[11]  U. Nowak,et al.  Numerical Integration of Constrained Mechanical Systems Using MEXX , 1995 .

[12]  Michel Géradin,et al.  Computational Aspects of the Finite Element Approach to Flexible Multibody Systems , 1993 .

[13]  R. Schwertassek,et al.  Dynamik flexibler Mehrkörpersysteme , 1999 .

[14]  Ahmed A. Shabana,et al.  Dynamics of Multibody Systems , 2020 .

[15]  Manuel S. Pereira,et al.  Computer-Aided Analysis of Rigid and Flexible Mechanical Systems , 1994 .

[16]  C. Farhat,et al.  A method of finite element tearing and interconnecting and its parallel solution algorithm , 1991 .

[17]  Werner Schiehlen,et al.  Advanced Multibody System Dynamics , 1899 .

[18]  Bernd Simeon,et al.  On computing smooth solutions of DAE'S for elastic multibody systems , 1999 .

[19]  J. Z. Zhu,et al.  The finite element method , 1977 .

[20]  K. Popp,et al.  Approximate Analysis of Flexible Parts in Multibody Systems Using the Finite Element Method , 1993 .